Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#17986048 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22586455 | C2 | semidirect |
| 5. C2×#349×C71 | C2 | semidirect |
| 40. #14556064 | D4 | semidirect |
| 158. C2×#349 | D71 | semidirect |
| 160. C71 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597949 | 2 |
| C2×#17986048 | 2 |
| #22590069 | 2 |
| #22586455 | 2 |
| C2×#349×C71 | 2 |
| #12998 | 71 |